Compressive sensing technology is widely applied in the field of image processing due to the expected balance of a compression ratio and a reconstruction quality, and has become a frontier and a hot one in the field of signal processing since its inception. Since there are redundancies in natural image signals, such as spatial redundancy caused by the correlation between adjacent pixels, time redundancy caused by the correlation between different frames, and spectral redundancy caused by the correlation of different color planes or spectrum bands, image signals can be compressed and reconstructed by employing the compressive sensing technology. However, existing reconstruction algorithms do not achieve a good balance between the reconstruction quality and the reconstruction speed, and they often focus on the reconstruction quality but not the reconstruction time. In such case, fixed subspace reconstruction algorithms have been proposed.
Subspace OMP algorithms are widely applied in practical engineering projects due to its simple structure, easy implementation, and low computation burden compared with other types of algorithms. These algorithms include OMP, StOMP, ROMP, CoSaMP, and SP algorithms. The size of the subspace in the OMP algorithm is 1, so that large number of iterations, heavy computation burden and low reconstruction speed will be caused when the sparsity K is too large. The StOMP algorithm can select multiple matching atoms in one iterative process, so that it can effectively reduce the number of iterations, further decrease the computation burden and reduce the reconstruction time. However, it strongly depends on the sparsity, resulting that a signal may not be correctly reconstructed if the sparsity K is not correctly estimated. The ROMP algorithm selects the atoms twice according to a correlation principle and a regularization process, however, the subspace selection in this algorithm depends not only on an intra-value correlation, but excessively depends on the sparsity K. Whether or not K is correctly estimated will affect the convergence speed and the reconstruction effect of the algorithm. The CoSaMP algorithm selects multiple uncorrelated atoms from an atom dictionary by means of backtracking and removes some uncorrelated atoms, and multiple matching atoms may be selected in one iteration. It is also necessary to know the sparsity K, however the real signal sparsity K is often unknown, and different principles on which the addition or removal of the atoms during each iteration of the CoSaMP algorithm are based will possibly result in incorrect estimation of the support set. The SP algorithm is a compromise of the above algorithms, and its performance is optimal among the above algorithms. The SP algorithm is low in computational complexity and high in reconstruction precision, and has a strict theoretical guarantee that when a measurement matrix A meets a restricted isometry property, the SP algorithm can accurately reconstruct any K-sparse signal from its noiseless measurements. But it has similar advantages and disadvantages with the CoSaMP algorithm.
All of the above algorithms adopt the concept of a fixed subspace. Except that the size of the subspace of the OMP algorithm is 1, sizes of other subspaces are all larger than 1, these algorithms make the number of iterations be reduced due to selection of multiple matching atoms at one time, thereby reducing the computation burden and the reconstruction time. However, they still fail to meet the real-time requirements, and the above algorithms are heavily dependent on the sparsity K, and whether or not K is correctly estimated will determine whether the signal can be correctly estimated or not as well as determine the reconstruction time of the signal. Meanwhile, selection of the dictionary subspace in these algorithms is based on the intra-value correlation, but does not take natural characteristic attributes of the image signal into account.